振动谱学研究中的光谱线型函数

本文讨论了在振动谱带计算拟合处理中的光谱线型函数问题,推导出适用于单道及多道拉曼光谱仪及色散型红外谱仪谱带线型公式。通过实验及拟合计算证实了它们的适用性并讨论了可能的误差源。理论计算和实验验证结果说明:在振动谱的谱带拟合计算中,应使用根据测谱条件计算求得的谱带线型函数,以保证拟合结果的可靠性。     

微加工薄膜变形镜特性分析

 借助测量微加工薄膜变形镜驱动器的面形影响函数，分析了驱动器的电压-位移函数和驱动器之间的线性叠加性;通过对连续面形变形镜拟合像差的理论分析和实验研究，建立了微加工薄膜变形镜电压解耦模型。分析了对前36阶Zernike模式的拟合残差和拟合能力，指出微加工薄膜变形镜仅可用来拟合低级像差并且有较大的拟合能力和较小的拟合残差，而不能拟合高级像差。     

A computer program for searching the best model for describing different experimental systems

An algorithm for searching the best polynomial analytical function for describing different experimental systems is presented. It is based

1. (1)on the generation of all possible analytical functions of a given order, with a given number of terms and with a given number of independent variables, and

2. (2)on the calculation of the parameters of all selected functions using the linear regression method.

To show the ability of the program two different examples are given:

1. (1) searching the best univariate polynomial model, and

2. (2) modelling of the stability of a two-component mixture as a function of three factors.

Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

一种新的珍珠层厚度测量方法

珍珠层厚度是是珍珠价值最主要的衡量指标之一,目前珍珠层厚度的无损测量方法主要采用光学相干层析成像技术和X射线技术。光学相干层析成像技术在实际测量时精度较低。在研究X射线测量原理的基础上,提出了一种新的珠层厚度测量方法。首先介绍了灰度图像的边缘识别算法和珍珠核、珍珠外圆度拟合算法,其次提出了一种引入对照机制的珍珠层测量算法,最后还对算法的误差进行了分析,算法的误差可以控制在0.02%以内。实际的测量也验证了本测量方法具有很高的精度。     

Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.     

OVID and SUPER: Two overlap programs for drug design

Summary Two programs, OVID and SUPER, for exploring the similarity of molecules with respect to their action at a receptor are described. OVID accepts two molecules as input and optimizes the three-dimensional overlap of specified atoms in one molecule with specified atoms in the second molecule. The result is expressed as a percent of the theoretical maximum. OVID gives a quantitative measure of the extent of a guessed correspondence between two molecules based on volume overlap of selected atoms. The Achilles' heel of OVID is that the correspondence between the two molecules has to be guessed. We realized that it would be better to systematically examine all possible correspondences of two structures to minimize the chance of overlooking a superior correspondence. We created SUPER to satisfy this need. SUPER accepts two molecules as input and finds the top twenty correspondences of their surfaces and charge distributions, giving a quantitative measure of the extent of each correspondence. An instructive example of the application of OVID and SUPER to the design of leukotriene D₄ receptor antagonists is described. SUPER appears to be a practical brainstorming tool for the medicinal chemist trying to understand how molecules whose structures may not resemble one another in an obvious way can bind to the same site.     

有限群的Sylow-子群的弱s-可补极大子群(英文)

假设G是一个有限群,H是G的一个子群.称H在G是s-置换的,若对G的任意的Sylow-子群Gp,有HG_p=G_pH:称H在G是弱s-可补的,若存在G的子群T使得G=HT且H∩T≤H_(sG),其中H_(sG)是所有包含在H中的G的s-置换子群生成的子群.本文给出了下列定理:设F是一个包含超可解群系u的饱和群系,有限群G有一个正规子群H使得G/H∈F.若F~*(H)的每个Sylow子群的所有极大子群在G中是弱s-可补的,其中F~*(H)是H的广义Fitting子群,则G∈F.它是J.Algebra,2007,315:192-209一文中的Skiba公开问题在极大子群情形下的肯定回答.     

超导低电阻接头衰减法测试过程中的拟合偏差控制

超导技术在许多高新技术领域有着广泛而深远的应用前景,其中超导导体接头技术是超导发展过程中必不可少的关键环节之一,快速而又准确地评估低电阻接头显得尤为重要.本文在考虑超导体的E-J特性后,针对目前低电阻接头采用的衰减法测量,计算得出感应电流完整的衰减曲线方程-幂函数方程.对比目前广泛采用的指数方程拟合与采用幂函数方程拟合的偏差,指出采用指数方程代替幂函数方程拟合的必要条件,为接头电阻衰减法测试,尤其是低电阻接头情况下的测量提供参考.     

On Fitting Ideals of Certain étale K-groups

Let F be an Abelian number field and S the set of primes of F that are either ramified or over p, with p an odd prime. In this paper we compute the (first) Fitting ideal of K _2i–2 ^ét (O _F ^S () for i 2, where O _F ^S is the ring of S-integers of F and is a character of Gal(F/) of order prime to p different from the ith power of the Teichmüller character. This Fitting ideal proves to be principal and generated by a Stickelberger element.